The identical statistical results for Data Sets 1, 2 and
3 certainly suggests that all three data sets may be equally well explained
by the same linear model. Let's look at this more closely. Using the link
on the left, open the Excel file containing the three data sets. Each data
set is on a separate Excel worksheet.

Task 1. For each data set,
create a separate scatterplot with a linear trendline.
How well does this linear model explain the relationship between X and Y
for each data set? What does this imply about the usefulness of using R2 or
R as the sole measure of a model's appropriateness?

Task 2. For all three data
sets, the value of R2 is relatively small. The linear
model of data from the module's introduction

on the other hand, has an R2 of 0.9997. Look carefully
at Data Set 2. Is there a mathematical model that might better
explain the relationship between X and Y? Remove the linear trendline and
try a more appropriate model. You should be able to find a model with an
R2 value of nearly 1.

Look carefully
at Data Set 3. It appears that the data are linear, so what is the reason
for the relatively small value for R2? Edit the data to remove
the problem and examine how this changes your model (if necessary, replot
the data). You should
be able to find a linear model with an R2 value
of nearly 1.